A short proof of the converse to the contraction principle and some related results

DOI10.12775/TMNA.2000.014zbMath0967.47035OpenAlexW2547413383MaRDI QIDQ1590134

Jacek R. Jachymski

Publication date: 19 December 2000

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.12775/tmna.2000.014

zbMATH Keywords

Bessaga's theoremconverse to the contraction principle

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functional equations for functions with more general domains and/or ranges (39B52) Systems of functional equations and inequalities (39B72) Axiom of choice and related propositions (03E25)

Related Items (8)

Revisiting Fryszkowski's problem ⋮ Stability of multivalued attractor ⋮ A converse of the Banach contraction principle for partial metric spaces and the continuum hypothesis ⋮ Fixed points and completeness in metric and generalized metric spaces ⋮ A generalization for a finite family of functions of the converse of Browder's fixed point theorem ⋮ Equivalence of completeness and contraction property ⋮ A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point. II ⋮ Converses to fixed point theorems of Zermelo and Caristi

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